Gary StudenASTR 4985/13/05Martian Crater Dating through IsochronsIntroductionThe universe is a vast and seemingly-endless array of space and matter thatharbors many mysteries. Through advances in technology, scientists have been able toexplore space and advance mankind’s understanding of the world around us. Arguablythe most studied object in the universe besides Earth is the planet Mars. The Mars GlobalSurveyor (MGS) is an orbiter that was launched in 1996 by N.A.S.A. and is designed tostudy the climate, atmosphere, topography, gravity, and other properties of Mars whilealso providing high resolution images of the surface. Unlike Earth, Mars has been largelygeologically inactive for a few billion years, which is reflected in the abundance of craterson the surface. Although craters may seem like mere holes in the ground, they serve theimportant function of being able to help scientists date planetary surfaces through craterdating. This process involves counting the number of craters in an area and using this toapproximate the age of the planetary surface. A large number of craters indicate an oldersurface while few craters suggest that the surface has been altered recently. Crater dating is an important process for two main reasons. First, it allowsscientists to be able to accurately date past stages of geologic activity on a planetarysurface. For example, if a surface is particularly saturated with craters and can be roughlydated, then it is possible to estimate the last eruption of a nearby volcano. As a result,scientists can determine if a planet is geologically active at all due to the presence ofcraters. Second, crater dating is a way to test various theories about the formation of thesolar system as well as stages within those theories. The heavy bombardment is a periodnear the end of the formation of the solar system when large planetesimals slammed intothe surfaces of planets and their moons. A surface that is extremely saturated withcraters, which is the result of being unaltered since heavy bombardment, is evidence forthe heavy bombardment stage of the widely accepted Nebular Theory. These theories canthen be applied to other various solar systems in the universe. Due to crater dating, thelocal testing of theories can be applied to systems throughout the galaxy.A convenient way to plot the measurements of craters is through the use ofisochrons. An isochron is a plot of crater size vs. crater density for one particular age.Parallel curves are created when multiple ages are plotted. When plotting isochrons, thelog of both the crater size and crater density is used to produce a straight isochron. Theisochrons that I am using were derived by William K. Hartmann. Hartmann attempted tocreate more precise isochrons and created the ones he used in his testing based on datafrom the Moon. One fact about craters accepted by scientists is that smaller cratersshould be more abundant than larger ones. Therefore, an inverse relationship existsbetween crater size and crater density. The main goal in my experiment of countingcraters is to have my data lie on an isochron or between two isochrons, which wouldallow me to estimate the age it best represents. It is particularly difficult to have my datamatch up exactly to an isochron that is plotted or that can be estimated because of thesmall size of my sample. However, if by eye, my data is generally linear once it is plotted,then I am able to approximate the various ages of the surfaces I sampled.DataAll of the data I used in my testing originates from the Malin Space ScienceSystems (MSSS), which extensively analyzed the data sent back by the MGS. Theimages referenced were taken by the Mars Orbital Camera (MOC) and then MSSSderived the various measurements applicable to the images, such as the length and width(in meters), pixel to meter conversion, and latitude and longitude of the image to name afew. These various derivations were placed into tables along with the images, which weregiven a name that I will reference. Particular information regarding MSSS and the MOCcan be ascertained from the MSSS website at http://www.msss.com/moc_gallery/. Thefollowing is information listing the crater name and the applicable data used that wasgathered from MSSS.CraterNameM03-00005R02-00837M01-00392R10-04230M12-00992M07-05058Longitudeof imagecenter180.10ºW6.46ºW 280.63ºW356.76ºW299.41ºW269.43ºWLatitude ofimagecenter34.76ºS 29.56ºS 20.98ºS 30.05ºS 29.32ºN 1.40ºNScale pixelwidth(meters)237.88 247.17 235.31 246.85 254.19 242.42Scaledimagewidth(kilometers)176.34 119.88 253.18 119.73 123.27 117.38Scaledimageheight(kilometers)253.72 119.93 1014.96 118.82 117.07 118.84AnalysisMeasurement of Crater Sizes The first step towards plotting my crater sizes involved physically counting andmeasuring the craters in the various images. Since I measured the craters by hand, thecraters had to physically be large enough in order to ascertain a proper measurement.Therefore, I had to create a limit as to how small the crater could be in order for my eyesto distinguish it properly. The smallest craters I decided to include in my data are around3-4 pixels in size. I used a tool for measuring distances, in pixels, in an image editingprogram called GIMP (http://www.gimp.org). In order to be as accurate as possible, Imeasured the diameter of the perceived long side of the crater and then the diameter ofthe angle perpendicular to the previous measurement. I then took the average of those twonumbers.Conversion to KilometersAll of the measurements that were made were done in pixels. Therefore, I had toconvert the various pixel sizes into kilometers before I plotted my data. As previouslystated, MSSS provided all of the necessary conversion information so I simply had to usethe scaled pixel width to convert all of my measurements. The scaled pixel width was inmeters, which required me to convert the meters into kilometers and then multiply theaverage pixel size of each crater by the scaled pixel width in kilometers. For example,one crater in the image M03-00005 averaged 14 pixels in size with a scaled pixel width inmeters of 237.88. Therefore, the calculation to convert the crater size into kilometers issimply (14*(237.88/1000)), which is 24.72 kilometers. Binning MethodThe process of binning involves placing the craters into various categories basedon their size. This is done in order to reduce the significance of each data